Certainly! Let's break down the problem step by step.
We know the following:
- The cost of a child’s meal ticket is [tex]$4.00.
- The cost of an adult’s meal ticket is $[/tex]12.00.
- A total of 1,650 meal tickets were sold.
- The total revenue from selling these tickets is $14,200.
We need to find the number of child tickets sold and the number of adult tickets sold.
Step 1: Define the variables.
- Let [tex]\( C \)[/tex] be the number of child tickets sold.
- Let [tex]\( A \)[/tex] be the number of adult tickets sold.
Step 2: Write the system of equations using the given information.
Equation 1: Total number of tickets sold
[tex]\[ C + A = 1650 \][/tex]
Equation 2: Total revenue from tickets sold
[tex]\[ 4C + 12A = 14200 \][/tex]
Step 3: Solve the system of equations.
First, we will solve for [tex]\( C \)[/tex] in terms of [tex]\( A \)[/tex] using Equation 1:
[tex]\[ C = 1650 - A \][/tex]
Next, substitute [tex]\( C = 1650 - A \)[/tex] into Equation 2:
[tex]\[ 4(1650 - A) + 12A = 14200 \][/tex]
Step 4: Simplify and solve for [tex]\( A \)[/tex].
Distribute the 4:
[tex]\[ 6600 - 4A + 12A = 14200 \][/tex]
Combine like terms:
[tex]\[ 6600 + 8A = 14200 \][/tex]
Subtract 6600 from both sides:
[tex]\[ 8A = 7600 \][/tex]
Divide by 8:
[tex]\[ A = 950 \][/tex]
So, there were 950 adult tickets sold.
Step 5: Substitute the value of [tex]\( A \)[/tex] back into Equation 1 to find [tex]\( C \)[/tex].
[tex]\[ C + 950 = 1650 \][/tex]
Subtract 950 from both sides:
[tex]\[ C = 700 \][/tex]
So, there were 700 child tickets sold.
Hence, the number of child tickets sold is 700 and the number of adult tickets sold is 950.
